Relashionship between RRIFs and Credit Limit

---

I. Introduction

---

Table 1.Sample for 5 randomly chosen households of the data set used in this study

TotalCreditLimit	After_tax_income	RRIFs
41000	185925	0
5000	35450	0
47500	42500	0
32000	33450	0
22000	57800	65000

II. Exploratory data analysis

---

Table 2: Summary for the Total credit limit on all credit cards owned

n	min	median	mean	max	sd
10996	125	16500	23667.51	340000	25638.52

Figure 2. Distribution for the Total credit limit on all credit cards owned by members the household

Figure 3. Distribution for the after-tax income of the household

Figure 4. Distribution for the Registered retirement income funds (RRIFs)

Figure 5. Interactive Scatterplot for the Total credit limit on all credit cards owned against after-tax income. The red line is the best fit line. The blue curve is the Loess curve.

Figure 6. Interactive Scatterplot for the Total credit limit on all credit cards owned against Registered retirement income funds (RRIFs). The red line is the best fit line. The blue curve is the Loess curve.

---

III. Multiple linear regression

i. Methods

Figure 7. Distribution for the Total credit limit on all credit cards owned raised to 0.333.

Using the following model:

## svyglm(formula = TotalCreditLimit_transf ~ RRIFs + After_tax_income, 
##     design = survey_design)

Figure 8. Normal Q-Qplot for the Total credit limit on all credit cards owned raised to 0.333

Figure 9. Residuals distribution for the statistical model

Figure 10. Residuals graph for the fitted values, with a Lowess curve in blue and a horizontal line at zero in red.

Figure 11. Residuals graph for After-tax income, with a Lowess curve in blue and a horizontal line at zero in red.

Figure 12. Residuals graph for the Registered retirement income funds (RRIFs), with a Lowess curve in blue and a horizontal line at zero in red.

Table 3: VIF table

	x
RRIFs	1.015446
After_tax_income	1.015446

---

ii. Model Results and Interpretation

Our model is the following:

\[ \begin{aligned}\widehat{Y}_{TCL}^{1/3} =& b_{0} + b_{RRIFs} \cdot (x_1) + b_{ATI} \cdot (x_2) \\ = & 20.77 + 0.000006 \cdot (x_1) + 0.00005 \cdot (x_2) \end{aligned} \]

---

Table 4: Summary Table:

Observations	10996
Dependent variable	TotalCreditLimit_transf
Type	Survey-weighted linear regression

R²	0.166212
Adj. R²	0.166060

	Est.	S.E.	t val.	p
(Intercept)	20.771786	0.267456	77.664254	0.000000
RRIFs	0.000006	0.000001	7.464255	0.000000
After_tax_income	0.000050	0.000003	14.746694	0.000000
Standard errors: Robust

\[\begin{aligned} H_0:&\beta_{0} = 0 \\\ \mbox{vs }H_A:& \beta_{0} \neq 0 \end{aligned}\] \[\begin{aligned} H_0:&\beta_{RRIFs} = 0 \\\ \mbox{vs }H_A:& \beta_{RRIFs} \neq 0 \end{aligned}\] \[\begin{aligned} H_0:&\beta_{ATI} = 0 \\\ \mbox{vs }H_A:& \beta_{ATI} \neq 0 \end{aligned}\]

Table 6: 95% Confidence intervals for the model coefficients.

##                         2.5 %       97.5 %
## (Intercept)      2.024758e+01 2.129599e+01
## RRIFs            4.655997e-06 7.971805e-06
## After_tax_income 4.319980e-05 5.644323e-05

---

iii. Inference for multiple regression

Table 7. ANOVA Table

## Anova table:  (Rao-Scott LRT)
## svyglm(formula = TotalCreditLimit_transf ~ RRIFs, design = survey_design)
##                     stats      DEff        df   ddf         p    
## RRIFs              5033.9     66.45      1.00 10994 < 2.2e-16 ***
## After_tax_income 136804.6    629.09      1.00 10993 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Table 8. The 95% Prediction intervals for the Total credit limit on all credit cards owned, raised to 0.333, where RRIFs = 0, 10, 10000, 500000, 1000000, respectively, for After-income tax median = 68625.

RRIF	Point estimate	SE
0e+00	24.19079	0.1009230
1e+01	24.19085	0.1009211
1e+04	24.25393	0.0993586
5e+05	27.34774	0.4120943
1e+06	30.50469	0.8289865

IV. Discussion

i. Conclusions

ii. Limitations

iii. Further questions

---

V. Citations and References